By using prism coupling to a square mu cavity, over 75% energy transfer to the whispering gallery modes (Q>10(6)) by frustrated total internal reflection was observed. A good comparison was found between measured data and theoretical model (based on a Fabry-Perot resonator), for the dependence of the coupling and linewidth of the whispering gallery modes (WGMs) as a function of relative separation between the prism and the mu cavity. By selecting the incident angle at the prism interface, the coupling to all four different sets of WGMs can be changed to coupling to only one set of WGMs. (C) 2003 American Institute of Physics.